Slightly wrong.
>>>Britain's departure from the European Union cannot be legally implemented without the terms approved by the House of Commons.<<<
Any exit deal cannot be implemented without Parliaments approval. To stop actually leaving the EU requires the Art.50 letter to be pulled and there probably is't a parliamentary majority to order that either, remember - 574 MPs were elected on a manifesto for implementing the referendum result.
We've dug ourselves into the biggest political catch-22 in UK history, we can either treat all public votes as binding or we set the precedent that politicians decide which public votes they can ignore and I can't think of anything that is more important than the EU issue.
(Short of asking us all 'Do we go to war', and don't say it'll never happen, parliament has only been voting on wars since Blair decided to cover his backside over Iraq)